Question

1. A researcher conducts a significance test every time she analyses a new data set. Over time, she conducts 100 tests.
2. 1. Suppose the null hypothesis is true in every case. What is the distribution of the number of times she rejects the null hypothesis at the level 0.05 level?
   2. Suppose she rejects the null hypothesis in seven of the tests. Is it plausible that the null hypothesis is correct in every case? Explain.

Answer 1

solution:

given data:

A researcher conducts a significance:-

a)

here we have 100 test with level of significance =0.05

since level of significance is defined as probability of rejecting H0 when H0 is true so

even if H0 is true then there is probability of rejecting H0 is 0.05

let X is number of test rejected so

X is binomial with n=100 and p=0.05

b)

since Probability of rejecting H0 even if its true is 0.05

and here 7 H0 are rejected let X is number of rejected H0 that in actual true so

X~Bin(7,0.05)

and we have to find P(X=7)

which is given by

Hence required probability is ZERO

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